We have undertaken mapping and spectroscopy of a broad range of type I post-Main-Sequence nebulae in CO J = 1 --> 0,J = 2 --> 1, and J = 3 --> 2, using the 12 m antenna at Kitt Peak, and the 45 m facility of the Nobeyama Radio Observatory. As a consequence, we find CO J = 2 --> 1 emission associated with NGC 3132 and NGC 6445, determine the location of CO J = 1 --> 0 emission in the nucleus of NGC 6302, and obtain (for the first time) CO J = 3 --> 2 spectroscopy for a substantial cross-section of type I sources. LVG analysis of the results suggests densities n(H-2) approximately 10(4) cm-3, and velocity gradients d-upsilon/dr approximately 2 x 10(2) in both NGC 7027 and CRL 618, commensurate with uniform expansion of a constant velocity outflow, whilst for the case of NGC 2346 these values probably exceed n(H-2) approximately 4.0 x 10(5) cm-3, d-upsilon/dr approximately 2.6 x 10(3) km s-1, and T(k) approximately 10(2) K, implying appreciable compression (and shock heating?) of the CO excitation zone. HI masses extend over a typical range 0.01 < M(HI)/M. < 1, whilst corresponding estimates of the progenitor mass imply 0.7 < M(prog)/M. < 2.3; values significantly in excess of those pertinent for normal PN, although somewhat at the lower end of the type I mass range. CO J = 3 --> 2 profiles for CRL 2688 confirm the presence of an extended plateau with width DELTA-upsilon approximately 85 km s-1, whilst modest J = 3 --> 2 spectrum for NGC 2346 appears to mimic lower-frequency results reasonably closely, confirming the presence of a double-peaked structure towards the core, and predominantly unitary profiles to the north and south, whilst there is also evidence to suggest appreciable J = 3 --> 2 asymmetry in CRL 618 compared to lower-frequency measures. The status of an extended cloud near HB 5 remains uncertain, although this clearly represents a remarkably complex region with velocity span DELTA-V approximately 50 km s-1. Our present J = 3 --> 2 results appear to track lower frequency measures extremely closely, implying local densities n(H-2) > 3 x 10(3) cm-3 - although temperatures close to the V(lsr) of HB 5 are relatively weak, and of order T(MB) (J = 3 --> 2) less-than-or-equal-to 0.9 K. Finally, as a result of both this, and previous investigations we find that of type I sources so far observed in CO, some approximately 42% appear to possess detectable levels of emission T(r)* > 0.1 K. Similarly, in cross-correlating this data with other results, we note a closely linear relation between J = 2 --> 1 antenna temperatures T(MB), and the surface brightness of H-2 S(1) quadrupole emission S(H-2)- a trend which appears also to be reflected between S(H-2) and corresponding parameters for [OI], [OII], [NI], [NII], and [SII]. Such relations almost certainly arise from comparable secular variations in line intensities, although the CO, H-2, and optical emission components are likely to derive from disparate line excitation zones. As a consequence, it is clear that whilst H-2 S(1) emission is probably enhanced as a result of local shock activity, the evidence for post-shock excitation of the CO and optical forbidden lines is at best marginal. Similarly, although it seems likely that CO emission derives from circum-nebular HI shells with kinetic temperature T(k) approximately 30 K or greater, the predominant fraction of low-excitation emission arises from a mix of charge exchange reactions, nebular stratification and, probably most importantly, the influence of UV shadow zones and associated neutral inclusions.